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8. Calculate and tabulate the vapor and liquid quantities to the base of Tray (D1 + I).

### Other Sidestream Product Draw Trays

The remaining sidestream draw trays are calculated by the same procedure as that outlined in the previous step. Remember that, in making partial pressure calculations, the presence of the next higher product vapor in the total vapor leaving the draw tray must be neglected. This principle is summarized in Table 2.4.

### Top Tray Calculations

The heat and material balance relationships at the top tray are determined by making a balance around Envelope III as shown on Figure 2.17. Figure 2.21 shows an expanded view of this section of the tower and gives the equations to be used in making the calculations. These equations are to be used in the following sequence.

1. Calculate the reflux heat above the top tray.

2. Calculate the heat removal capability of the available reflux.

3. Calculate the amount of reflux from the condenser which is required to absorb the excess heat at Tray N as Lj^ and convert it to moles per hour.

4. Calculate the mole fraction of hydrocarbon product vapor in the total vapor leaving the top tray, neglecting the hydrocarbon portion of the distillate vapor product.

5. Calculate the hydrocarbon partial pressure of the overhead distillate liquid plus reflux in the total vapor leaving Tray N. Convert the atmospheric dew point of the distillate liquid product to this partial pressure. If this calculated temperature does not check the value originally assumed, assume a new temperature and repeat the procedure.

6. Calculate the reflux induced on the top tray. Induced reflux is the amount of vapor from Tray (N - 1) which enters and is condensed on Tray N for the purpose of raising the reflux liquid from its temperature leaving the reflux drum to that of the top tray.

7. Calculate and tabulate the vapor and liquid quantities at Tray N.

### Condenser Calculations and Overall Heat Balance

The condenser duty is calculated by making a heat balance around Envelope IV in Figure 2.17. An expanded view of this calculation is given in Figure 2.21. Note that, in Figure 2.21, Qc is also calculated by an overall system heat balance. The two values should check to within 2 percent of the absolute value of Q If not, a serious error has been made somewhere in the calculations, and the work must be repeated until a satisfactory check is obtained.

### Fractionation Capability of the System

Having completed the heat and material balance calculations around the atmospheric tower and its auxiliaries, it must now be determined whether or not the fractionation specifications can be met with the resulting configuration of trays and reflux. The reflux which exists in the tower is determined principally by the definition of the material balance and is influenced relatively little by draw tray locations. Because of tray pressure drop, a slight variation in calculated temperatures will result by altering draw tray locations, but, unless the change in configuration is drastic, say by four trays or more, the effect on reflux will be slight, certainly by less than 10 percent. Thus, for all practical purposes, reflux in a Type U system may be defined as constant for a given material balance. Referring back to figures 2.6 and 2,7, the technique for analyzing fractionation capability is outlined by the following procedure.

1. Since Packie's reflux ratio is defined in terms of liquid falling from a draw tray, calculate the reflux from all draw trays and from the top tray by making a heat balance around the system at all trays below these just mentioned. These temperatures on the trays below draw trays are arrived at by the assumption of linear temperature variation between draw trays. Calculate these reflux flows as both moles and volumes.

2. Calculate the reflux ratio as the volume of reflux from the draw tray per volume of total product vapors entering the draw tray. The separation factor, F, is the product of this reflux ratio and the number of actual trays in the section.

3. Calculate the difference between the ASTM 50 volume percent temperatures of the product and that of the total remaining lighter products.

4. From Packie's curves, read the ASTM (5-95) Gap for the various separations and compare them with the required values.

For a Type U system using conventional numbers of trays between draw trays and requiring normal separations, there will always be an excess of "trays x reflux". This leads to the conclusion that, by removing heat from the system at points relatively low in the tower, one can reduce reflux and thus reduce tower size while still being able to meet fractionation specifications. This leads into the study of the two types of towers employing heat removal systems.

Another facet of the results of the analysis of fractionation capability is that, in the Type U calculation example, there appears to be a slight imbalance between the various sections. While there is more than enough "trays x reflux" for the required separations, the conditions in the heavy naphtha-light distillate section has considerably less excess "trays x reflux" than do all the other sections. This implies an incorrect choice of draw tray location.

### Summary of Vapor-Liquid Traffic

Tabulate the flows of vapor and liquid at all key trays in the tower as moles per hour. Plot these values versus tray number as vapor from tray and liquid to tray. This plot will be of great assistance in tower sizing calculations.

Heat and Material Balance Calculations for Type R Towers

A complete Type R tower is shown in Figure 2.22. This drawing illustrates the basic process and its essential auxiliaries as well as the external heat and material balance quantities. In this type of installation, sidestream draw trays are total draws, i.e., the total liquid leaving the draw tray-sidestream product plus reflux to the tray below—is withdrawn from the tower. The reflux is pumped back to the tower after cooling rather than overflowing internally from the draw tray to the tray below as in the case of Type U and Type A systems. Figure 2.22 will be the basis for discussing the heat and material balance calculations in this section.

The method of splitting the draw tray exit liquid upstream of the product stripper is the preferred arrangement from the viewpoint of operating economy. The alternate processing arrangement allows the total liquid to flow to the stripper. The stripped liquid is cooled and then split into product and pumpback reflux. While the former arrangement requires two sets of pumps and heat exchangers as opposed to only one set required by the latter, the additional operating cost for stripping the reflux more than offsets the differences in capital investment. In most cases, the pumpback reflux will be a significantly greater volume than the product. In view of this, stripping of reflux in addition to the product will require total heat inputs to the strippers considerably greater than that required for stripping only products. If steam stripping were used rather than reboiling, this would necessitate a significantly greater atmospheric tower diameter as well as larger facilities for boiler feedwater treating and for handling of foul condensate from the tower overhead.

This section outlines procedures for calculating product draw tray temperatures at all points in the system and for making an overall heat balance around the tower. The method is based upon assuming a draw tray temperature and then calculating the internal reflux required by the system's heat balance. This internal reflux to the draw tray defines the hydrocarbon product partial pressure in the vapor above the tray. Converting the 14.7 psia bubble point of the unstripped liquid to this partial pressure gives a temperature which must check the assumed value. The top tray temperature is calculated by the same procedure, except that the reference temperature is the 14.7 psia dew point of the gross overhead product.

Preliminary Steps

At this point, it is assumed that the following have been fully defined.

1. Complete hydrocarbon material balance for feed and products.

2. Steam rates to stripping sections and steam distribution between overhead distillate vapor and liquid.

3. Hydrocarbon material balances around product strippers.

4. Atmospheric EFV temperatures for products corresponding to the estimated stripout for each product.

5. Draw tray locations, number of trays in each section and total number of trays in the tower.

6. Heat input to the base section of the tower from feed and bottoms stripping steam, heat outflow in the bottoms liquid and external heat quantities at the flash zone. This bottoms-section heat balance is shown on Envelope 1 in Figure 2.22.

All these items must be completed before proceeding further with calculations.

Estimate of Tower Operating Conditions

Draw tray temperatures are estimated from the correlation of Figure 2.23. The following form the basis for this chart.

1. Flash zone pressure = 24.7 psia.

2. Overflash = 2.0 volume percent of feed.

3. Reduced crude and lowest sidestream are steam stripped at 10 pounds steam per barrel of product, measured as 60 degree F liquid.

4. All other sidestreams are reboiled equivalent to steam stripping at 10 pounds per barrel.

5. Cooled, unstripped pumpback reflux is used at each sidestream draw tray.

6. For sidestream products, use the estimated bubble point of unstripped liquid from the draw trays. For overhead product, use the calculated dew point.

Note carefully the restrictions which apply and the indicated temperature variations which will occur as the process conditions differ from the stipulated bases.

1. An increase in flash zone pressure will increase draw tray temperatures.

2. An increase in overflash will slightly decrease draw tray temperatures of the second sidestream product and all others above.

3. An increased stripping steam rate will decrease product draw tray temperatures due to the reduced hydrocarbon partial pressures.

4. Use of stripping steam in all product strippers rather than in only the first sidestream stripper will decrease draw tray temperatures of the second sidestream and all others above.

5. Stripping of reflux in addition to stripping the product will increase heat input to the system. If this is by

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